Activity 5. Angle of Inclination. 22 January \( 20 z 5 \) 1. Determine the indination of the line. Round your answer to 2 decimal places with points \( A\left(3 ; \frac{7}{2}\right) \) \( B(-8 ;-2) \). 2. Determine the angle of inclination (correct to 1 decimal place) of the straight line through \( (2 ; 1) \neq(-3 ;- \) 3. Find the angle \( \theta \) and round off your answer to \( z \) decimal places if appropriate.

Sure, let's address each part of your problem step by step. ### **1. Determine the Inclination of the Line Through Points \( A(3, \frac{7}{2}) \) and \( B(-8, -2) \)** **Step 1: Calculate the Slope (\( m \)) of the Line** The slope of a line passing through two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Plugging in the coordinates: \[ m = \frac{-2 - \frac{7}{2}}{-8 - 3} = \frac{-\frac{11}{2}}{-11} = \frac{11}{2 \times 11} = \frac{1}{2} \] **Step 2: Determine the Angle of Inclination (\( \alpha \))** The angle of inclination is the angle the line makes with the positive \( x \)-axis, calculated using the arctangent of the slope: \[ \alpha = \arctan(m) = \arctan\left(\frac{1}{2}\right) \] Using a calculator: \[ \alpha \approx 26.565^\circ \] **Step 3: Round the Angle** Rounded to two decimal places: \[ \alpha \approx 26.57^\circ \] **Answer:** The inclination of the line is **26.57 degrees**. --- ### **2. Determine the Angle of Inclination of the Straight Line Through \( (2, 1) \) and \( (-3, \, \text{?}) \)** It seems there might be a typo or missing information in this part of the question. Specifically, the coordinates for the second point are incomplete: \( (-3, - ) \). **To proceed, please provide the complete coordinates of the second point.** --- ### **3. Find the Angle \( \theta \) and Round Off Appropriately** This part also appears to be incomplete or missing specific details required to solve the problem, such as: - The points defining the line or additional information about \( \theta \). - The value of \( z \) indicating to how many decimal places to round the answer. **Please provide the missing details so I can assist you effectively.** --- Feel free to provide the additional information, and I'll be happy to help you with the remaining parts of your problem!